Bags are needed to hold accessories or other objects on to the bicycle. It is desirable that, when installed on the bicycle, the bag stays with the bicycle and does not bounce around or up and down such that the bag does not interfere with the riding, especially during intensive mountain-bicycle riding. A Bicycle bag is often attached to the bicycle through additional fasteners such as straps or hook-and-loop fasteners. These fasteners provide places for water, mud, or dirt to collect and build up on the bag from riding. The build-up mud or dirt is hard to clean and also scratches the paint on the bicycle when the mud or dirt bounces with the bag and rubs against the bicycle frame during riding. Further, the failure of the fasteners causes the bag to lose all of its utility as a non-interfering storage container.